CN107678433B - Loading and unloading equipment scheduling method considering AGV collision avoidance - Google Patents

Loading and unloading equipment scheduling method considering AGV collision avoidance Download PDF

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CN107678433B
CN107678433B CN201710984769.5A CN201710984769A CN107678433B CN 107678433 B CN107678433 B CN 107678433B CN 201710984769 A CN201710984769 A CN 201710984769A CN 107678433 B CN107678433 B CN 107678433B
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CN107678433A (en
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王洋洋
朱瑾
魏亚茹
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Shanghai Maritime University
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    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
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Abstract

The invention provides a dispatching method of loading and unloading equipment considering AGV collision avoidance. Establishing a dynamic model and two types of collision avoidance models of container terminal loading and unloading equipment; dynamically regarding discrete events of equipment as a scheduling problem of a mixed flow shop, and then scheduling all container tasks of the mixed flow shop by adopting an integral graph sequence method; and finally, under the condition of considering two collision avoidance situations, according to an introduced layered control structure, sending each generated operation time window to a stage controller by a state monitoring controller, distributing each operation time window to specific equipment by the stage controller, and updating the operation time of the AGV according to the minimum time control problem so as to realize collision-free scheduling of all tasks of the AGV. The scheduling method considering AGV collision avoidance and loading and unloading equipment simultaneously can meet the optimization requirement of scheduling and managing problems of a large-scale automatic container terminal.

Description

Loading and unloading equipment scheduling method considering AGV collision avoidance
Technical Field
The invention relates to the field of transportation of an automatic container terminal, in particular to the field of dispatching of loading and unloading equipment of the automatic container terminal, and particularly relates to a method for dispatching the loading and unloading equipment by considering AGV collision avoidance.
Background
The problem of AGV trajectory planning in container terminals has received a lot of attention from researchers due to the close connection between devices and the complexity of the environment. At present, the dispatching of container terminal loading and unloading equipment usually ignores the actual trajectory planning problem of the equipment. In addition, in the research of container terminals, the devices are generally assumed to work without interference, and the scheduling scheme does not include interference caused by collision avoidance. In addition, some researchers have studied the traditional three-stage hybrid flow shop of an automated container terminal to consider only the single quay crane case, whereas in the actual terminal environment, the job usually involves multiple quay bridges, multiple AGVs and multiple bridges. In addition, the research does not comprehensively consider the interaction between the collision avoidance constraint of the AGV and the dispatching of the loading and unloading equipment, which can influence the dispatching optimization performance of the loading and unloading equipment at the container terminal; based on the method, the invention provides a loading and unloading equipment scheduling method considering AGV collision avoidance to optimize the problem of collision-free scheduling of a shore bridge, the AGV and a field bridge in the process of transporting containers.
Disclosure of Invention
The invention provides a loading and unloading equipment scheduling method considering AGV collision avoidance aiming at the problem of collision-free scheduling of loading and unloading equipment of an automatic container terminal, so as to realize collision-free scheduling of a terminal shore bridge, the AGV and a yard bridge. Firstly, establishing a dynamic model of a container terminal loading and unloading device and two types of collision avoidance models, wherein the dynamic model of a transport container can be represented by the combination of high-level discrete event dynamics and low-level continuous time dynamics, the scheduling of the loading and unloading device is related to the high-level discrete event dynamics, and the collision-free track planning is related to the low-level continuous time dynamics; dynamically regarding discrete events of equipment as a scheduling problem of a mixed flow shop, and then scheduling all container tasks of the mixed flow shop by adopting an integral graph sequence method; and finally, introducing a hierarchical control structure, determining the task sequence of each stage and minimizing the completion time of all tasks of each stage by a state monitoring controller under the condition of considering two collision avoidance constraints, sending the generated operation time windows to a stage controller, distributing the operation time windows to specific equipment by the stage controller, and updating the operation time of the AGV according to the minimum time control problem to realize collision-free scheduling of all tasks of the AGV.
Scheduling, as considered in this patent, includes determining the order of tasks for each particular device and the operating time window for each task; the scheduling is determined by dealing with a hybrid flow shop scheduling problem and an AGV collision avoidance problem. Two types of collision avoidance are considered: a stationary collision, which refers to the collision of the AGVs with stationary obstacles and associated equipment in front of the delivery point of the stacking area, and a moving collision, which refers to the collision of different AGVs with each other during the transportation of the container. The method for dispatching the loading and unloading equipment mainly comprises the following steps:
step one, establishing a model of three-stage equipment
In the three stage flow shop, a task is defined as a complete process of transporting a container from a ship to a designated location in a heap.
(1) Stage 1: multiple QCs
(2) And (2) stage: multiple AGV
(3) And (3) stage: multiple ASCs
Assuming that there are N containers to be transported from ship to heap, let Φ be the set of tasks (| Φ | ═ N), introduce two virtual task points 0 and N +1, and then let Φ be defined1Φ ∪ {0} and Φ2Φ ∪ { N +1 }. the time constraint for a particular device is as follows：
Figure BDA0001440267280000021
Figure BDA0001440267280000022
Figure BDA0001440267280000023
Figure BDA0001440267280000024
Figure BDA0001440267280000025
Figure BDA0001440267280000026
Figure BDA0001440267280000027
Figure BDA0001440267280000028
Figure BDA0001440267280000029
Figure BDA00014402672800000210
Figure BDA00014402672800000211
Figure BDA00014402672800000212
In the formula, a pair
Figure BDA00014402672800000213
j ∈ Φ (i ≠ j), defining the decision variables:
xij1 indicates that in the first phase, the container task i completes earlier than task j, otherwise, xij＝0；
y ij1 indicates that in the second phase, the container task i completes earlier than task j, otherwise, yij＝0；
z ij1 indicates that in the third phase, the container task i completes earlier than task j, otherwise zij＝0；
aiIs the completion time of container task i in the first phase; biIs the completion time of the container task i in the second stage; c. CiIs the completion time of the container task i in the third phase; diIs the start time for the transition from task i to task j in the second phase; e.g. of the typeiAGV arrival time at which container i is ready to be transported in the first stage;
Figure BDA0001440267280000031
is that
Figure BDA0001440267280000032
Completion time of h1∈{1,2,3}，h2∈{1,2}；
Figure BDA0001440267280000033
Is the transfer time of container i to container j handled by the designated AGV in the second phase; r is a large positive number; at is the reserved time for two containers to be loaded and unloaded successively by the same ASC.
Inequalities (1) and (4) represent the first task to initialize the QC and AGV, respectively. Inequality (2) represents a relationship between task i and task j processed by QC; inequality (3) ensures that at any moment, the joint point before each QC has at most one AGV; inequalities (5) and (6) represent the start of the second phase after task i is completed in the first phase; inequalities (7) and (8) indicate that task i is started in the third phase after completion of the second phase; inequality (9) represents the relationship between container task j and task i handled by ASC; inequality (10) indicates that the reserved time delta t between two successive tasks is ensured under the constraint of only one AGV at most at the front junction of each heap at any moment; inequalities (11) and (12) represent the transitions of container tasks i and j transported by the AGV.
Because collision avoidance is considered, decision variables of various tasks cannot be determined simultaneously, and a graphical method can be adopted to represent the three-stage hybrid flow shop scheduling, wherein each graphical representation processes corresponding container tasks in a specific order at a specific stage; integer variable xij，yijAnd zijRespectively defining the sequence of the container tasks processed by specific equipment in the three stages; x is the number ofij，yijAnd zijThe values of (a) may be represented by a graph of the stages;
the graphic sequence S represents the scheduling sequence of all container tasks to be executed in a specific stage of the hybrid flow shop; for phase 1, define
Figure BDA0001440267280000034
Wherein task j is executed after task i; for task i and task j, if task i and task j are accessed sequentially and both task i and task j are executed by a particular device in the graph, then xij1, otherwise xij0; stages 2 and 3 are defined similarly;
in order to schedule all container tasks of the mixed flow workshop in sequence, an overall graph sequence of each stage of the three stages is needed, and the index number of the sequence gives the operation sequence of the tasks; therefore, consider introducing a continuous variable bi(i e Φ), each task of the overall graph sequence being related to the values of these variables; it will be apparent that the variable values may be arranged in an ascending order to determine the job order of the tasks. And in the three-stage hybrid plant mentioned in step one, if there is R (1-x)ij)+bj＞biThen, the sequence S {.. ·, i., j. } (b) }j≥biI, j e Φ, i ≠ j) is a feasible whole graph sequence. The reason is as follows:
consider an approximationBundles (7), (8) and (10) having R (1-z)ij)+bj＞dj≥biSo that R (1-z)ij)+bj＞bi. Because task i and task j are accessed sequentially for a particular AGV, R (1-y) may be obtainedij)+bj＞bi. Thus, for the sequence S {.. ·, i., j. } (b)j≥bi,i,j∈Φ,i≠j)，R(1-xij)+bj＞bi，R(1-yij)+bj＞biAnd R (1-z)ij)+bj＞bi. This means that the sequence S is a feasible overall pattern sequence.
Step two, establishing an AGV and a collision avoidance model
1) Establishing AGV dynamic model
All AGVs use a point-quality model to estimate the dynamic behavior of a two-dimensional space
Figure BDA0001440267280000041
Figure BDA0001440267280000042
In the formula, AGVpIs at a position of
Figure BDA0001440267280000043
Speed is
Figure BDA0001440267280000044
Acceleration of a vehicle
Figure BDA0001440267280000045
(up(k)∈R2)，I2Is a 2 × 2 unit array, Δ t is the time interval;
the constraints on AGV speed and acceleration are as follows:
Figure BDA0001440267280000046
Figure BDA0001440267280000047
Figure BDA0001440267280000048
in the formula umaxAnd vmaxUpper limit values of acceleration and velocity, respectively, and M is an arbitrary number.
2) Establishing static collision avoidance constraint model
The rectangular area may be represented by the lower left corner coordinate(s)low，x，slow，y) And coordinates of upper right corner(s)high，x，shigh，y) To represent; to avoid the static obstacle area, the position of AGVi must be outside the rectangular area; therefore, the constraint conditions for satisfying the collision avoidance requirement are as follows:
Figure BDA0001440267280000049
Figure BDA00014402672800000410
with binary variables introduced, the constraint (18) can be rewritten to the form of a standard optimization problem as follows:
Figure BDA0001440267280000051
Figure BDA0001440267280000052
wherein R is a large positive real number, bin,τ(k) Is a binary variable; constraints (19) and (20) ensure that at least one of equations (18) is true;
3) establishing a moving collision avoidance constraint model
In each time interval, except for the AGVp1And AGVp2Are different from each other, a minimum safety distance (2d) is maintained between them; the collision avoidance constraint can be written in the form of:
Figure BDA0001440267280000053
Figure BDA0001440267280000054
p2∈[1,...,nagv]，p1≠p2in the formula (I), the compound is shown in the specification,
Figure BDA0001440267280000055
and
Figure BDA0001440267280000056
p of AGV in k1And p2The position of (a); introducing a binary variable, the constraint (21) can be rewritten as follows:
Figure BDA0001440267280000057
Figure BDA0001440267280000058
in the formula, bm,τIs a binary variable, R is a sufficiently large positive real number, and equations (20) and (21) ensure that equation (19) holds;
step three, determining a hierarchical control structure
According to the hierarchical control structure, the collision-free scheduling of all tasks is planned by the whole graph sequence, and the whole graph sequence simultaneously solves the problem of collision-free track planning and the scheduling of loading and unloading equipment; according to the overall graph sequence, sequentially completing collision-free scheduling of all tasks one by one; for a group of tasks with an operation sequence to be determined, the first planned task is used for determining the relevant collision-free track of the task in the phase 2 and the relevant operation time of the task in the phase 1 and the phase 3 controlled by a high-level controller; after the first task is completed, the high-level controller updates the discrete event dynamic and determines the operation sequence and the operation time of the rest tasks again; this process is repeated until the scheduling of all tasks is completed;
1) state monitoring controller
The state monitoring controller is used for determining the task sequence of each stage and minimizing the completion time of all tasks of each stage. When the QC and the AGV can be scheduled at any time, the completion time is defined as the completion time of the last ship leaving task. I.e., max { a }1,...,an,e1,...enI.e., | f | ceiling∞，||·||∞Denotes an infinite norm, wherein f ═ a1,a2,...,an,e1,...,en]T。
In order to determine the task order of all stages of the mixed flow shop problem, the theorem needs to add additional constraints; the following definitions are first made:
a＝[a1,a2,...,an]T
b＝[b1,b2,...,bn]T
c＝[c1,c2,...,cn]T
d＝[d1,d2,...,dn]T
e＝[e1,e2,...,en]T
Figure BDA0001440267280000061
Figure BDA0001440267280000062
Figure BDA0001440267280000063
the scheduling problem model can be written as:
Figure BDA0001440267280000064
constraint conditions are as follows:
Figure BDA0001440267280000065
and (1) - (12) and associated equation constraints;
Figure BDA0001440267280000066
and
Figure BDA0001440267280000067
are interdependent between
Figure BDA0001440267280000068
And
Figure BDA0001440267280000069
start time between transitions
Figure BDA00014402672800000610
Or
Figure BDA00014402672800000611
Dependent on the interaction between the devices performing task i; this interaction is implemented by a high-level controller that solves the following optimization problem:
Figure BDA00014402672800000612
constraint conditions are as follows: (1) (12) and associated equality constraints; the optimization problem is a linear programming problem, so that the time of the hybrid flow shop can be quickly adjusted;
2) phase controller
Considering the consistency of the dynamic models of all AGVs in stage 2, an AGV set is defined: Ψagv＝{1,2,...,nagv}
fagv:Φ→Ψagv, (25)
Wherein f isagvIs to map the task set Φ to the AGV set ΨagvA function of (a); f. ofagv(i) Assigned to task iThe AGV of (1); the time window assigned to AGV task i is noted as
Figure BDA0001440267280000071
And
Figure BDA0001440267280000072
for QC and ASC, the mapping of task i to devices is predetermined, since each container has a defined start and end position on board and on the stack; by fqc(i) And fyc(i) To represent the QC and ASC assigned to task i; the time window allocated to QC task i is then noted as
Figure BDA0001440267280000073
And
Figure BDA0001440267280000074
similarly, the time window assigned to the ASC task j is noted as
Figure BDA0001440267280000075
And
Figure BDA0001440267280000076
3) low-level controller
In this minimum time problem, the AGV is required to complete the operation as quickly as possible while taking into account the stationary obstacle and the moving obstacle
Figure BDA0001440267280000077
And
Figure BDA0001440267280000078
numerical method is adopted to calculate the original point state r of the AGV to the container0Transport to target state rfThe shortest time of (d); selecting r from the intersection of QC and ASC for task i0And rf；
During the transportation of task j from the bank side to the stack, the selection is based on QCfqc(i) And ASCfyc(i) Is determined by the task allocation of (c). And after task i is completed, at AGV returns from the stack to the shore side in the process of loading task j (y)ij1) starting and ending points also depend on fqc(i) And fyc(i) In that respect Let T be the width of a given time window. At known time intervals [ 0.,. T-1 ]]Inner, AGVpThe target state r can only be reached at a specific momentfThis is determined by a binary variable at time k. The constraint is as follows:
Figure BDA0001440267280000079
Figure BDA00014402672800000710
Figure BDA00014402672800000711
in the formula, bp(k) E {0,1} is a binary variable, R is a sufficiently large positive real constraint only if bp(k) Equation (26) of 1 is true; the formulas (21) and (27) are restricted when bp(k) When the value is 1, ensuring that the AGV reaches the target position r from the initial state r (k)f；
Assuming that t (k) is a time difference from time 0 to time k (t (k) ═ k), when b (k) ═ 1, (k) b (k) is the completion time of the operation; obtaining the shortest time from the starting point to the end point of the AGV by solving the minimum value of the total completion time; it is also possible to consider improving the energy efficiency of trajectory planning and according to the minimum cost factor λ in the objective functionengMinimizing the sum of the accelerations to achieve a minimum time for the AGV to travel from the start point to the end point; thus, the minimum time optimization problem can be written as follows:
Figure BDA0001440267280000081
constraint conditions are as follows: (11) (15), (17), (18), (20), (21) and (26), (27).
Wherein u ═ u (0), u (1),.. times, u (T-1)]TRepresenting a continuous decision variable, b ═ bp(0),bp(1),...,bp(T-1)]TA binary decision variable.
The invention has the following effects and advantages:
the invention changes a single shore bridge into a plurality of shore bridges on the basis of generally defined three-stage flow shop scheduling, realizes the operation sequence of related equipment of the mixed flow shop by adopting an integral graph sequence method, and combines an introduced integral graph sequence to plan the collision-free scheduling of all tasks according to a determined layered control structure while considering two AGV collision avoidance constraints, wherein the integral graph sequence simultaneously solves the problems of loading and unloading equipment scheduling and collision-free track planning. The performance and efficiency of handling and transporting containers by the loading and unloading equipment under the condition that AGV collision avoidance constraint is considered in the automatic container terminal are effectively improved.
Drawings
FIG. 1 is a sequence diagram of three equipment shipping containers
FIG. 2 is a schematic diagram of the sequential decision of 6 executing tasks in three stages
FIG. 3 is a schematic diagram of an approximate speed limit for an AGV
FIG. 4 is a schematic diagram of a safety zone of an AGV
FIG. 5 is a schematic view of a static obstacle area
FIG. 6 is a schematic diagram of a hierarchical control structure
FIG. 7 is a schematic diagram of the overall structure of a two-layer controller
TABLE 1 time window for three-stage operation
TABLE 2 selection of start and end points for task i
Detailed Description
Step one, establishing a model of three-stage equipment
In the present invention, consider the multiple QC, multiple AGV and multiple ASC scenarios for an automated container terminal. The operation of three types of equipment can be considered a three stage hybrid flow shop. In a hybrid flow shop, each task performed goes through several stages of processing. Each stage of the same device may process a portion of a task in parallel. The processing sequence of each task is the same and the processing time of each stage of each task is fixed. In the three stage flow shop, a task is defined as a complete process of transporting a container from a ship to a designated location in a heap.
(1) Stage 1: multiple QCs
(2) And (2) stage: multiple AGV
(3) And (3) stage: multiple ASCs
The three-stage hybrid plant is defined with all operations as shown in figure 1. Pi 1Defined as the position of the container i on the ship, Pi 2And
Figure BDA0001440267280000091
defined as QC to AGV delivery point location, Pi 3Defined as the location of the delivery point, P, from AGV to ASCi 4Defined as the storage location of the container i in the stacking area.
Figure BDA0001440267280000092
Indicating QC no-load slave Pi 2To Pi 1，
Figure BDA0001440267280000093
Indicating QC full load from Pi 1To Pi 2；
Figure BDA0001440267280000094
Indicating AGV is fully loaded from Pi 2To Pi 3，
Figure BDA0001440267280000095
Indicating AGV is unloaded from Pi 3Return to Pi 2And
Figure BDA00014402672800000921
Figure BDA0001440267280000096
indicating ASC full load from Pi 3To Pi 4，
Figure BDA0001440267280000097
Indicating ASC idle slave Pi 4Return to Pi 3。
Assuming that there are N containers to be transported from ship to heap, let Φ be the set of tasks (| Φ | ═ N), introduce two virtual job points 0 and N +1, and then define Φ1Φ ∪ {0} and Φ2Φ ∪ { N +1 }. the time constraint for a particular device is as follows:
Figure BDA0001440267280000098
Figure BDA0001440267280000099
Figure BDA00014402672800000910
Figure BDA00014402672800000911
Figure BDA00014402672800000912
Figure BDA00014402672800000913
Figure BDA00014402672800000914
Figure BDA00014402672800000915
Figure BDA00014402672800000916
Figure BDA00014402672800000917
Figure BDA00014402672800000918
Figure BDA00014402672800000919
in the formula, a pair
Figure BDA00014402672800000920
j ∈ Φ (i ≠ j), defining the decision variables:
xij1 indicates that in the first phase, the container task i completes earlier than task j, otherwise, xij＝0；
y ij1 indicates that in the second phase, the container task i completes earlier than task j, otherwise, yij＝0；
z ij1 indicates that in the third phase, the container task i completes earlier than task j, otherwise zij＝0；
aiIs the completion time of container task i in the first phase; biIs the completion time of the container task i in the second stage; c. CiIs the completion time of the container task i in the third phase; diIs the start time for the transition from task i to task j in the second phase; e.g. of the typeiAGV arrival time at which container i is ready to be transported in the first stage;
Figure BDA0001440267280000101
is that
Figure BDA0001440267280000102
Completion time of h1∈{1,2,3}，h2E {1,2} represents the operating time window of task i, as shown in Table 1;
Figure BDA0001440267280000103
is the transfer of container i to container j handled by a given AGV in the second stageTime; r is a large positive number; at is the reserved time for two containers to be loaded and unloaded successively by the same ASC.
Inequalities (1) and (4) represent the first task to initialize the QC and AGV, respectively. Inequality (2) represents a relationship between task i and task j processed by QC; inequality (3) ensures that at any moment, the joint point before each QC has at most one AGV; inequalities (5) and (6) represent the start of the second phase after task i is completed in the first phase; inequalities (7) and (8) indicate that task i is started in the third phase after completion of the second phase; inequality (9) represents the relationship between container task j and task i handled by ASC; inequality (10) indicates that the reserved time delta t between two successive tasks is ensured under the constraint of only one AGV at most at the front junction of each heap at any moment; inequalities (11) and (12) represent the transitions of container tasks i and j transported by the AGV.
In accordance with the above constraints, the discrete event dynamics of a three-stage device is considered a hybrid flow shop scheduling problem. These decision variables may be determined by the state monitor by solving a hybrid flow shop scheduling problem. Since the decision variables for the various tasks cannot be determined simultaneously due to collision avoidance considerations, the three-stage hybrid flow shop schedule may be represented using a graphical approach, where each graphical representation processes the corresponding container tasks in a particular order at a particular stage. Integer variable xij，yijAnd zijThe order in which a particular device processes container tasks in the three phases is defined separately. x is the number ofij，yijAnd zijAs shown in fig. 2, an example of 6 container tasks being processed (involving 2QC,3AGV and 3ASC) is given to illustrate the sequence of tasks that each device may process for each phase, where the container tasks being processed ① - ⑥, the virtual container origin task
Figure BDA0001440267280000104
Virtual container destination task ⑦, with different arrow paths representing different devices as in stage 1, tasks ① and ③ are processed in sequence by one QC and tasks ④ and ⑥ are processed in sequence by another QCThe QCs are processed in sequence, and the first two tasks, task ① and task ④, are processed by the two QCs, and the last two tasks, task ③ and task ⑥, are processed by the two QCs.
Figure BDA0001440267280000111
TABLE 1 time Window for three-stage operation
The graphical sequence S represents all container tasks that are to be performed at a particular stage of the hybrid flow shop. For phase 1, define
Figure BDA0001440267280000112
Where task j is executed after task i. For task i and task j, if task i and task j are accessed sequentially and both task i and task j are executed by a particular device in the graph, then xij1, otherwise xijOne possible graphics order in phase 1 is (①, ④, ④, ④.) for example, task ④ and task ④ are accessed sequentially by the same device, but task ② is not processed after task ④ because task ② and task ④ 1 are not processed by the same device.for a particular phase, there may be multiple graphics orders.for another graphics order for phase 1 may be (④).
In order to schedule all the container tasks of the mixed flow shop in sequence, an overall graph sequence of each stage of the three stages is required, and the index numbers of the arrangement sequence give the operation sequence of the tasks. Therefore, consider introducing a continuous variable bi(i e.di), each task of the overall graph sequence is related to the value of these variables. It will be apparent that the variable values may be arranged in an ascending order to determine the job order of the tasks. And in the three-stage hybrid plant mentioned in step one, if there is R (1-x)ij)+bj＞biThen, the sequence S {.. ·, i., j. } (b) }j≥biI, j e Φ, i ≠ j) is a feasible whole graph sequence. The reason is as follows:
considering constraints (7), (8) and (10), there is R (1-z)ij)+bj＞dj≥biSo that R (1-z)ij)+bj＞bi. Because task i and task j are accessed sequentially for a particular AGV, R (1-y) may be obtainedij)+bj＞bi. Thus, for the sequence S {.. ·, i., j. } (b)j≥bi,i,j∈Φ,i≠j)，R(1-xij)+bj＞bi，R(1-yij)+bj＞biAnd R (1-z)ij)+bj＞bi. This means that the sequence S is a feasible overall pattern sequence.
Step two, establishing an AGV and a collision avoidance model
1) Establishing AGV dynamic model
Assuming that the dynamic models of each AGV are consistent, all AGVs use the point-quality model to estimate the dynamic behavior of the two-dimensional space
Figure BDA0001440267280000121
Figure BDA0001440267280000122
In the formula, AGVpIs at a position of
Figure BDA0001440267280000123
Speed is
Figure BDA0001440267280000124
Acceleration of a vehicle
Figure BDA0001440267280000125
(up(k)∈R2)，I2Is a 2 × 2 unit array, Δ t is the time interval.
The speed and acceleration constraints are as follows:
Figure BDA0001440267280000126
Figure BDA0001440267280000127
Figure BDA0001440267280000128
in the formula umaxAnd vmaxUpper limit values for acceleration and velocity, respectively. To simplify the calculations, the constraints on velocity and acceleration both approximate a polygonal constraint using linear equations. The constraints on speed and acceleration are as follows:
Figure BDA0001440267280000129
Figure BDA00014402672800001210
Figure BDA00014402672800001211
wherein M is an arbitrary number. As shown in FIG. 3, a graphical maximum speed approximation of an AGV is presented. The X-axis and Y-axis represent the range of lateral and longitudinal speeds of the AGV, respectively. Circles represent exact constraints, while polygons represent approximate constraints.
2) Establishing static collision avoidance constraint model
Assuming that the AGVs occupy a square safety zone, AGV2, d is the safety distance of a single AGV area, each having a side length of 2d and an area of 2 d. As shown in FIG. 4, a schematic diagram of the safety zone of a single AGV is presented.
As shown in fig. 5, a schematic view of the static obstacle area is given. Assume that FIG. 5(a) is a schematic view of two stationary obstacle areas near a stack, where container 1, AGV2, and landing bridge stationary track 3; the coordinate diagram of the rectangular area of the two tracks of the static obstacle field bridge (ASC) is shown in FIG. 5(b), and the rectangular area can be represented by the coordinates(s) at the lower left cornerlow，x，slow，y) And coordinates of upper right corner(s)high，x，shigh，y) To indicate. To avoid stationary obstacle zones, AGViMust be outside the rectangular area. Therefore, it isThe constraint conditions that satisfy the collision avoidance requirement are as follows:
Figure BDA00014402672800001212
Figure BDA0001440267280000131
with binary variables introduced, the constraint (18) can be rewritten to the form of a standard optimization problem as follows:
Figure BDA0001440267280000132
Figure BDA0001440267280000133
wherein R is a large positive real number, bin,τ(k) Is a binary variable. Constraints (19) and (20) ensure that at least one of equations (18) is true, thus ensuring that the AGV is outside of the stationary obstacle area.
3) Establishing a moving collision avoidance constraint model
When multiple AGVs transport a container to different destinations, collisions that may occur between the AGVs need to be considered. In each time interval, except for the AGVp1And AGVp2Are different from each other, a minimum safety distance (2d) is maintained between them.
The collision avoidance constraint can be written in the form of:
Figure BDA0001440267280000134
Figure BDA0001440267280000135
p2∈[1,...,nagv],p1≠p2in the formula (I), wherein,
Figure BDA0001440267280000136
and
Figure BDA0001440267280000137
respectively, the k-th step of AGVp1And AGVp2The position of (a). Introducing a binary variable, the constraint (21) can be rewritten as follows:
Figure BDA0001440267280000138
Figure BDA0001440267280000139
in the formula, bm,τIs a binary variable, R is a real number, and equations (22) and (23) ensure that equation (21) holds true.
Step three, determining a hierarchical control structure
Based on the dynamic decomposition of the above system, a hierarchical control structure of the container terminal is required to coordinate the phase controllers, as shown in fig. 6, (i.e., high-level controller and low-level controller). The high-level controller comprises a state monitoring controller and a stage controller of each stage. The condition monitoring controller coordinates the three-stage device by determining the sequence and timing of tasks and schedules time windows for each stage's operation. The phase controller assigns a time window for each operation to a particular device. The lower level controllers include respective local controllers. The local controllers are associated with specific devices (QC, AGV and ASC).
According to the hierarchical control structure, the collision-free scheduling of all tasks is planned by the whole graph sequence, and the whole graph sequence simultaneously solves the problems of scheduling of the loading and unloading equipment and planning of collision-free tracks. According to the overall graph sequence, the collision-free scheduling of all tasks is completed sequentially one task after another. For a set of tasks for which an operational sequence is to be determined, the first task planned is used to determine the relevant collision-free trajectory for that task in phase 2, and the relevant operational time for that task in phases 1 and 3, controlled by the higher level controller. After the first task is completed, the high-level controller updates the discrete event dynamics and re-determines the operation sequence and operation time of the remaining tasks. This process is repeated until the scheduling of all tasks is completed. As shown in fig. 7, a schematic diagram of the overall structure of the interaction of the two-layer controller is given.
1) State monitoring controller
The state monitoring controller is used for determining the task sequence of each stage and minimizing the completion time of all tasks of each stage. When the QC and the AGV can be scheduled at any time, the completion time is defined as the completion time of the last ship leaving task. I.e., max { a }1,...,an,e1,...enI.e., | f | ceiling∞，||·||∞Denotes an infinite norm, wherein f ═ a1,a2,...,an,e1,...,en]T。
To determine the order of tasks for all stages of the hybrid flow shop problem, the theorem adds additional constraints. The following definitions are made:
a＝[a1,a2,...,an]T
b＝[b1,b2,...,bn]T
c＝[c1,c2,...,cn]T
d＝[d1,d2,...,dn]T
e＝[e1,e2,...,en]T
Figure BDA0001440267280000141
Figure BDA0001440267280000142
Figure BDA0001440267280000143
the scheduling problem model can be written as:
Figure BDA0001440267280000144
constraint conditions are as follows:
Figure BDA0001440267280000145
and (1) - (12) and associated equation constraints.
When planning the operation of a particular task, the order of operation of the task(s) ((
Figure BDA0001440267280000151
And
Figure BDA0001440267280000152
) Will not change. In particular, it is possible to use, for example,
Figure BDA0001440267280000153
and
Figure BDA0001440267280000154
are interdependent between
Figure BDA0001440267280000155
And
Figure BDA0001440267280000156
start time between transitions
Figure BDA0001440267280000157
Or
Figure BDA0001440267280000158
Depending on the interaction between the devices performing task i. This interaction is implemented by a high-level controller for solving the following optimization problem:
Figure BDA0001440267280000159
constraint conditions are as follows: (1) and (12) and the associated equation constraints. The optimization problem is a linear programming problem, so that the time of the hybrid flow shop can be adjusted quickly.
2) Phase controller
The phase controller assigns each task to a particular device of the respective phase according to the sequence of tasks to be derived. In the hybrid flow shop scheduling problem, this allocation relationship is implicit in the equation constraint, for which the following three mapping functions are defined.
Considering the consistency of the dynamic models of all AGVs in stage 2, an AGV set is defined: Ψagv＝{1,2,...,nagv}。
fagv:Φ→Ψagv(27)
Wherein f isagvIs to map the task set Φ to the AGV set ΨagvAs a function of (c). f. ofagv(i) The AGV assigned to task i. The time window assigned to AGV task i is noted as
Figure BDA00014402672800001510
And
Figure BDA00014402672800001511
for QC and ASC, the mapping of task i to devices is predetermined, since each container has a defined start and end position on board and on the stack. By fqc(i) And fyc(i) To indicate the QC and ASC assigned to task i. The time window allocated to QC task i is then noted as
Figure BDA00014402672800001512
And
Figure BDA00014402672800001513
similarly, the time window assigned to the ASC task j is noted as
Figure BDA00014402672800001514
And
Figure BDA00014402672800001515
3) low-level controller
By solving a minimum time control problem, AGVAnd the low-level controller realizes collision-free track scheduling of the AGV. In this minimum time problem, the AGV is required to complete the operation as quickly as possible while taking into account the stationary obstacle and the moving obstacle
Figure BDA00014402672800001516
And
Figure BDA00014402672800001517
numerical method is adopted to calculate the original point state r of the AGV to the container0Transport to target state rfThe shortest time of (c). Selecting r from the intersection of QC and ASC for task i0And rf。
The exact choice of start and end points for task i is shown in table 2. During the transportation of task j from the bank side to the stack, the selection is based on QCfqc(i) And ASCfyc(i) Is determined by the task allocation of (c). And after task i is completed, in the process that AGV returns from stack to shore side and loads task j (y)ij1) starting and ending points also depend on fqc(i) And fyc(i) In that respect Let T be the width of a given time window. At known time intervals [ 0.,. T-1 ]]Inner, AGVpThe target state r can only be reached at a specific momentfThis is determined by a binary variable at time k. The constraint is as follows:
Figure BDA0001440267280000161
Figure BDA0001440267280000162
Figure BDA0001440267280000163
in the formula, bp(k) E {0,1} is a binary variable, R is a sufficiently large positive real constraint only if bp(k) Equation (28) of 1 is true. Formula (23) and formula (29) are bound when bp(k) When the value is 1, ensuring that the AGV reaches the target position r from the initial state r (k)f。
Figure BDA0001440267280000164
TABLE 2 selection of start and end points for task i
Assuming that t (k) is a time difference from time 0 to time k (t (k) ═ k), when b (k) ═ 1, t (k) b (k) is the completion time of the operation. And solving the minimum value of the total completion time to obtain the shortest time from the starting point to the end point of the AGV. It is also possible to consider improving the energy efficiency of trajectory planning and according to the minimum cost factor λ in the objective functionengThe sum of the accelerations is minimized to achieve the minimum time for the AGV to travel from the start point to the end point. Thus, the minimum time optimization problem can be written as follows:
Figure BDA0001440267280000165
constraint conditions are as follows: (13) (17), (19), (20), (22), (23) and (28), (29).
Wherein u ═ u (0), u (1),.. times, u (T-1)]TRepresenting a continuous decision variable, b ═ bp(0),bp(1),...,bp(T-1)]TA binary decision variable. Solving the optimization problem, the result of which is used to update the operation time
Figure BDA0001440267280000166
And
Figure BDA0001440267280000167
thus determining the start time of the next job for the AGV.

Claims (1)

1. A method for dispatching loading and unloading equipment considering AGV collision avoidance comprises the steps that constraint conditions of the considered collision avoidance comprise static collision and moving collision; the static collision refers to the collision between the AGV and a static obstacle and related equipment near a delivery point in front of the stacking area, and the moving collision refers to the collision between the two AGVs in the process of transporting the container; the scheduling considered includes determining the task order for each particular QC, AGV and ASC and the operating time window for each task; the scheduling is determined by processing a scheduling problem of a hybrid flow shop and an AGV collision avoidance problem, and the collision-free scheduling of a shore bridge, the AGV and a field bridge is realized by combining an integral graph sequence; the method for dispatching the loading and unloading equipment for AGV collision avoidance is characterized by comprising the following steps of:
step one, establishing a model of three-stage equipment
In the three-stage flow shop, a task is defined as a complete process of transporting a container from a ship to a specified position in a stacking area;
(1) stage 1: multiple QCs
(2) And (2) stage: multiple AGV
(3) And (3) stage: multiple ASCs
Assuming that there are N containers to be transported from ship to heap, let Φ be the set of tasks (| Φ | ═ N), introduce two virtual job points 0 and N +1, and then define Φ1Φ ∪ {0} and Φ2Phi ∪ { N +1}, the time constraint for a particular device is as follows:
Figure FDA0002416451060000011
Figure FDA0002416451060000012
Figure FDA0002416451060000013
Figure FDA0002416451060000014
Figure FDA0002416451060000015
Figure FDA0002416451060000016
Figure FDA0002416451060000017
Figure FDA0002416451060000018
Figure FDA0002416451060000019
Figure FDA00024164510600000110
Figure FDA00024164510600000111
Figure FDA0002416451060000021
in the formula, a pair
Figure FDA0002416451060000022
Defining decision variables:
xij1 indicates that in the first phase, the container task i completes earlier than task j, otherwise, xij＝0；
yij1 indicates that in the second phase, the container task i completes earlier than task j, otherwise, yij＝0；
zij1 indicates that in the third phase, the container task i completes earlier than task j, otherwise zij＝0；
aiIs the completion time of container task i in the first phase; biIs the completion time of the container task i in the second stage; c. CiIs the completion time of the container task i in the third phase; diIs the start time for the transition from task i to task j in the second phase; e.g. of the typeiIs the AGV arrival time of the first stage ready to transport container i；
Figure FDA0002416451060000023
Is that
Figure FDA0002416451060000024
Completion time of h1∈{1,2,3}，h2∈{1,2}；
Figure FDA0002416451060000025
Represents the corresponding container operation, wherein h1∈{1,2,3}，h2∈{1,2}，
Figure FDA0002416451060000026
Indicating QC no-load slave Pi 2To Pi 1，
Figure FDA0002416451060000027
Indicating QC full load from Pi 1To Pi 2；
Figure FDA0002416451060000028
Indicating AGV is fully loaded from Pi 2To Pi 3，
Figure FDA0002416451060000029
Indicating AGV is unloaded from Pi 3Return to Pi 2And
Figure FDA00024164510600000210
Figure FDA00024164510600000211
indicating ASC full load from Pi 3To Pi 4，
Figure FDA00024164510600000212
Indicating ASC idle slave Pi 4Return to Pi 3；
Figure FDA00024164510600000213
Is the transfer time of container i to container j handled by the designated AGV in the second phase; r is a large positive number; Δ t is the reserved time for two containers to be loaded and unloaded successively by the same ASC;
inequalities (1) and (4) represent the first task of initializing the QC and the AGV, respectively; inequality (2) represents a relationship between task i and task j processed by QC; inequality (3) ensures that at any moment, the joint point before each QC has at most one AGV; inequalities (5) and (6) represent the start of the second phase after task i is completed in the first phase; inequalities (7) and (8) indicate that task i is started in the third phase after completion of the second phase; inequality (9) represents the relationship between container task j and task i handled by ASC; inequality (10) indicates that the reserved time delta t between two successive tasks is ensured under the constraint of only one AGV at most at the front junction of each heap at any moment; inequalities (11) and (12) represent the transitions of container tasks i and j transported by the AGV;
graphically representing the three-stage hybrid flow shop schedule, wherein each graphical representation processes corresponding container tasks in a particular order at a particular stage; integer variable xij，yijAnd zijRespectively defining the sequence of the container tasks processed by specific equipment in the three stages; x is the number ofij，yijAnd zijThe values of (a) may be represented by a graph of the stages;
the graphic sequence S represents the scheduling sequence of all container tasks to be executed in a specific stage of the hybrid flow shop; for phase 1, define
Figure FDA00024164510600000214
Wherein task j is executed after task i; for task i and task j, if task i and task j are accessed sequentially and both task i and task j are executed by a particular device in the graph, then xij1, otherwise xij0; stages 2 and 3 are defined similarly;
taking into account the introduction of a continuous variable bi(iE Φ), each task of the overall graph sequence is related to the values of these variables; obviously, in a three stage hybrid plant, if R (1-x) is presentij)+bj＞biThen, the sequence S {.. ·, i., j. } (b) }j≥biI, j ∈ Φ, i ≠ j) is a feasible overall graph sequence; and the variable values can be arranged according to an ascending method to determine the operation sequence of the tasks;
step two, establishing an AGV and a collision avoidance model
1) Establishing AGV dynamic model
All AGVs use a point-quality model to estimate the dynamic behavior of a two-dimensional space
Figure FDA0002416451060000031
Figure FDA0002416451060000032
In the formula, AGVpIs at a position of
Figure FDA0002416451060000033
Speed is
Figure FDA0002416451060000034
Acceleration of a vehicle
Figure FDA0002416451060000035
(up(k)∈R2)，I2Is a 2 x 2 unit array, Δ T is the reserved time to load and unload two containers in succession by the same ASC, T is the width of a given time window, i.e. assuming a known time interval [0]；
The constraints on AGV speed and acceleration are as follows:
Figure FDA0002416451060000036
Figure FDA0002416451060000037
Figure FDA0002416451060000038
in the formula umaxAnd vmaxUpper limit values of acceleration and velocity, respectively, M being an arbitrary number;
2) establishing static collision avoidance constraint model
The rectangular area may be represented by the lower left corner coordinate(s)low，x，slow，y) And coordinates of upper right corner(s)high，x，shigh，y) To represent; to avoid the static obstacle area, the position of AGVi must be outside the rectangular area; therefore, the constraint conditions for satisfying the collision avoidance requirement are as follows:
Figure FDA0002416451060000039
Figure FDA00024164510600000310
with binary variables introduced, constraint (16) can be rewritten into the form of a standard optimization problem as follows:
Figure FDA0002416451060000041
Figure FDA0002416451060000042
in the formula, d is the safety distance of a single AGV region, the side length of the region is 2d, and the area of the region is 2d multiplied by 2 d; r is a very large positive real number, bin,τ(k) Is a binary variable; constraints (17) and (18) ensure that at least one of equations (16) is true;
3) establishing a moving collision avoidance constraint model
In each time interval, except for the AGVp1And AGVp2Are different from each other,a minimum safety distance 2d is kept between the two; the collision avoidance constraint can be written in the form of:
Figure FDA0002416451060000043
Figure FDA0002416451060000044
p2∈[1,...,nagv]，p1≠p2in the formula
Figure FDA0002416451060000045
And
Figure FDA0002416451060000046
p of AGV in k1And p2The position of (a); introducing a binary variable, the constraint (19) can be rewritten as follows:
Figure FDA0002416451060000047
Figure FDA0002416451060000048
in the formula, bm,τIs a binary variable, R is a sufficiently large positive real number, and equations (20) and (21) ensure that equation (19) holds;
step three, determining a hierarchical control structure
According to the hierarchical control structure, the collision-free scheduling of all tasks is planned by the whole graph sequence, and the whole graph sequence simultaneously solves the problem of collision-free track planning and the scheduling of loading and unloading equipment; according to the overall graph sequence, sequentially completing collision-free scheduling of all tasks one by one; for a group of tasks with an operation sequence to be determined, the first planned task is used for determining the relevant collision-free track of the task in the phase 2 and the relevant operation time of the task in the phase 1 and the phase 3 controlled by a high-level controller; after the first task is completed, the high-level controller updates the discrete event dynamic and determines the operation sequence and the operation time of the rest tasks again; this process is repeated until the scheduling of all tasks is completed;
1) state monitoring controller
The state monitoring controller is used for determining the task sequence of each stage and minimizing the completion time of all tasks of each stage; when the QC and the AGV can be scheduled at any time, the completion time is defined as the completion time of the last ship leaving task; i.e., max { a }1,...,an,e1,...enI.e., | f | ceiling∞，||·||∞Denotes an infinite norm, wherein f ═ a1,a2,...,an,e1,...,en]T；
In order to determine the task order of all stages of the mixed flow shop problem, the theorem needs to add additional constraints; the following definitions are first made:
a＝[a1,a2,...,an]T
b＝[b1,b2,...,bn]T
c＝[c1,c2,...,cn]T
d＝[d1,d2,...,dn]T
e＝[e1,e2,...,en]T
Figure FDA0002416451060000051
Figure FDA0002416451060000052
Figure FDA0002416451060000053
the scheduling problem model can be written as:
Figure FDA0002416451060000054
constraint conditions are as follows:
Figure FDA0002416451060000055
and (1) - (12) and associated equation constraints;
between
Figure FDA0002416451060000056
And
Figure FDA0002416451060000057
start time between transitions
Figure FDA0002416451060000058
Or
Figure FDA0002416451060000059
Dependent on the interaction between the devices performing task i; this interaction is implemented by a high-level controller that solves the following optimization problem:
Figure FDA00024164510600000510
constraint conditions are as follows: (1) (12) and associated equality constraints; the optimization problem is a linear programming problem, so that the time of the hybrid flow shop can be quickly adjusted;
2) phase controller
Considering the consistency of the dynamic models of all AGVs in stage 2, an AGV set is defined: Ψagv＝{1,2,...,nagv}
fagv:Φ→Ψagv, (25)
Wherein f isagvIs to map the task set Φ to the AGV set ΨagvA function of (a); f. ofagv(i) An AGV assigned to task i; the time window assigned to AGV task i is noted as
Figure FDA0002416451060000061
And
Figure FDA0002416451060000062
for QC and ASC, use fqc(i) And fyc(i) To represent the QC and ASC assigned to task i; the time window allocated to QC task i is then noted as
Figure FDA0002416451060000063
And
Figure FDA0002416451060000064
similarly, the time window assigned to the ASC task j is noted as
Figure FDA0002416451060000065
And
Figure FDA0002416451060000066
3) low-level controller
In this minimum time problem, the AGV is required to complete the operation as quickly as possible while taking into account the stationary obstacle and the moving obstacle
Figure FDA0002416451060000067
And
Figure FDA0002416451060000068
numerical method is adopted to calculate the original point state r of the AGV to the container0Transport to target state rfThe shortest time of (d); selecting r from the intersection of QC and ASC for task i0And rf；
The selection is based on QCf during the course of task j being shipped from the bank side to the stackqc(i) And ASCfyc(i) Is determined by the task allocation of (c); and after task i is completed, in the process that AGV returns from stack to shore side and loads task j (y)ij1), start and endThe point also depends on fqc(i) And fyc(i) (ii) a Assuming that T is the width of a given time window, T-1 is applied at known time intervals [0]Inner, AGVpThe target state r can only be reached at a specific momentfThis is determined by a binary variable at time k; the constraint is as follows:
Figure FDA0002416451060000069
Figure FDA00024164510600000610
Figure FDA00024164510600000611
in the formula, bp(k) E {0,1} is a binary variable, R is a sufficiently large positive real number, constrained only if bp(k) Equation (26) of 1 is true; the formulas (21) and (27) are restricted when bp(k) When the value is 1, ensuring that the AGV reaches the target position r from the initial state r (k)f；
Assuming that t (k) is a time difference from time 0 to time k (t (k) ═ k), when b (k) ═ 1, (k) b (k) is the completion time of the operation; obtaining the shortest time from the starting point to the end point of the AGV by solving the minimum value of the total completion time; it is also possible to consider improving the energy efficiency of trajectory planning and according to the minimum cost factor λ in the objective functionengMinimizing the sum of the accelerations to achieve a minimum time for the AGV to travel from the start point to the end point; thus, the minimum time optimization problem can be written as follows:
Figure FDA0002416451060000071
constraint conditions are as follows: (11) - (15), (17), (18), (20), (21) and (26), (27);
wherein u ═ u (0), u (1),.. times, u (T-1)]TRepresenting a continuous decision variable; b ═ bp(0),bp(1),...,bp(T-1)]TRepresenting binary blocksA policy variable.
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